Open problems in geometry of numbers, and the geometry of quantum phases

数几何和量子相几何中的未决问题

• 批准号: 5355-2007
• 负责人: Erdahl, Robert
• 金额: $ 0.73万
• 依托单位: Queen's University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2010
• 资助国家: 加拿大
• 起止时间: 2010-01-01 至 2011-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=449804
• 关键词: Open; problems; geometry; numbers; quantum

The first part of my program is to investigate fundamental questions in the theory of lattices and geometry of numbers. I have been able to introduce new methods into these classical theories, which in two instances resulted in answering question posed by Voronoi nearly 100 years ago. I have also established links between some classical results in geometry of numbers and a variety of modern mathematical topics. The long-range goal is to understand more clearly the geometry of lattices in higher dimensional spaces, such as 6, 8, or even 20.

我的计划的第一部分是调查在格理论和几何数字的基本问题。 我已经能够引入新的方法到这些经典理论，这在两个实例中导致回答问题提出的Voronoi近100年前。 我还建立了一些经典的结果之间的联系几何的号码和各种现代数学的主题。 长期目标是更清楚地理解更高维空间（如6维、8维甚至20维）中的晶格几何。